Collateralization, leverage, and stressed expected loss

We describe a general equilibrium model with a banking system in which the deposit bank collects deposits from households and the merchant bank provides funds to firms. Merchant banks borrow collateralized short-term funds from deposit banks. In a financial downturn, as the value of collateral decreases, the merchant bank must sell assets on short notice, reinforcing the crisis, and default if their cash buffer is insufficient. The deposit bank suffers from loss because of the depreciated assets. If the value of the deposit bank's assets is insufficient to cover deposits, it also defaults. Deposits are insured by the government. The premium paid by the deposit bank is its expected loss on the deposits. We define the bank's capital shortfall in the crisis as the expected loss on deposits under stress. We calibrate the model on the U.S. economy and show how this measure of stressed expected loss behaves. In the absence of regulation, a 40% decline of the securities market would induce a loss of 17.8% in the ex-ante value of the assets or 80.7% of the ex-ante value of the equity